Programmer's ROM - The Computer Language Library/programmersrom.iso/ada/piwg/z000004.ada

Text File | 1988-05-03 | 12.7 KB | 289 lines

with PHYSICAL_REAL ; use PHYSICAL_REAL ;

package PHYSICAL_UNITS_BASIC is

-- This package specification defines Ada types for physical
-- quantities. A number of other packages use this package
-- specification in order to provide a comprehensive dimension
-- checking and units conversion system.
--
--              PHYSICAL QUANTITIES AND THEIR ASSOCIATED DIMENSIONS
--
--   Errors can occur in writing equations to solve problems in classical
--physics. Many of these errors can be prevented by performing a dimensionality
--check on the equations. All physical quantities have a fundamental dimension
--that is independent of the units of measurement. The basic physical dimensions
--are: length, mass, time, electrical charge, temperature and luminous intens-
--ity.There are a number of systems of units for measuring physical quantities.
--The MKS system is based on meter, kilogram, second  measurement.
--The CGS system is based on centimeter, gram, second  measurement.
--The English system is based on feet, pound, second  measurement.
--A few physical dimensions and the associated measurement unit in
--these three systems are :
--
--
--      Physical Quantity                           Unit System
--        Dimension                         MKS         CGS          English
--
--        length                            meter       centimeter   feet
--
--        mass                              kilogram    gram         pound mass
--
--        time                              second      second       second
--
--        force                             newton      dyne         poundal
--
--        energy                            joule       erg          B.t.u.
--
--
--   The checking of a physical equation has two aspects. The first is to check
--the dimensionality. The dimensionality is independent of the unit system. The
--second is to check that a consistent system of units is used in the equation.
--   An example of a dimensionality check is using the basic equation F=ma to
--determine that force has the dimension  mass x length / time squared, then
--              2
--check if  F=mv /r  is dimensionally correct. The check is performed by
--expanding the dimensions, e.g.  mass x (length/time) x (length/time) / length.
--with the dimensions expected for force from the basic equation F=ma. As
--expected, centripetal force has the same dimensionality as the force from
--Newton's second law of motion.
--
--                    THE ALGEBRA OF DIMENSIONALITY
--
--   The dimension of any physical quantity can be written as
--
--                  a   b   c   d   e   f
--                 L   M   T   Q   C   K
--
--where a,b,c,d,e and f are integers such as -4, -3, -2 , -1, 0, 1, 2, 3, 4
--and L is length, M is mass, T is time, Q is charge, C is luminous intensity
--and K is temperature. An exponent of zero means the dimension does not apply
--to the physical quantity. The normal rules of algebra for exponents apply
--for combining dimensions.
--
--   In order to add or subtract two physical quantities the quantities must
--have the same dimension. The resulting physical quantity has the same
--dimensions. Physical quantities with the same dimension in different
--systems of units can be added or subtracted by multiplying one of
--the quantities by a units conversion factor to obtain compatible units.
--
--   The multiplication of two physical quantities results in a new physical
--quantity that has the sum of the exponents of the dimensions of the initial
--two quantities.
--
--   The division of one physical quantity by another results in a new physical
--quantity that has the dimension of the exponents of the first quantity minus
--the exponents of the second quantity.
--
--   Taking the square root of a physical quantity results in a new physical
--quantity having a dimension with exponents half of the initial dimension.
--
--   Raising a physical quantity to a power results in a new physical quantity
--having a dimension with the exponents multiplied by the power.
--
--                                     2                2  2    2 -2
--          e.g. v has dimension L/T, v  has dimension L /T or L T
--
--   The derivative of a physical quantity with respect to another physical
--quantity results in a new physical quantity with the exponents of the
--first dimension minus the exponents of the other dimension.
--         e.g.  v has dimension L/T, t has dimension T,
--
--                                           2
--               then dv/dt has dimension L/T
--
--   The integral of a physical quantity over the range of another physical
--quantity results in a new physical quantity that has a dimension with the
--sum of the exponents of the two quantities.
--
--         e.g.  v has dimension L/T, t has dimension T,
--               then  integral v dt  has dimension  L/T * T or L
--
--
-- The initial thought was to have metric units and English units
-- in separate package specifications. This proved inpractical
-- because time in seconds is both metric and English. Many other
-- units such as watt of power and Farad of capacitance are in
-- both systems. A further impracticallity arose when considering
-- the design of a units system conversion package. e.g. A package
-- that would provide accurate conversion form meters to inches
-- to micrometers to light years. The one package specification became
-- so large that it was inefficient, so, in order to keep the size
-- reasonable, three packages were created. The basic units, the
-- mechanical units and the electrical units. Then a package
-- called other units came into existance for pragmatic reasons.
--
-- Notice that there is not a type called LENGTH because
-- adding length in meters to length in feet is not allowed.
-- Even LENGTH_METRIC and LENGTH_ENGLISH are not acceptable
-- because meters can not be added to centimeters and inches can
-- not be added to feet. Further complication arises because of
-- seconds of time and seconds of arc. There can be ounces of
-- milk ( liquid measure ) and ounces of sugar ( weight measure ).
-- There can be quarts of milk and quarts of strawberries ( dry
-- measure ). Thus the decision was made that every Ada type
-- would be a dimension name followed by a unit name.
--
-- Now, more choices had to be made. Unit names such as
--  DENSITY_KILOGRAM_PER_CUBIC_METER or DENSITY_TONS_PER_CUBIC_YARD
-- start getting long and there are many combinations. The number
-- of combinations for density are all the units of mass times all
-- the units of volume. Thus a subset of all possible units was
-- chosen with the additional short hand notation of _MKS for
-- the meter, kilogram, second system of units and the _ENGLISH for
-- the foot, pound, second system. Additional qualifiers are added
-- to clarify such as VOLUME_QUART_LIQUID and VOLUME_QUART_DRY.
--
-- Some other compromises were made:
--       Only a few units were entered as both singular and plural.
--       The choice of names is the authors. A committee could expand
--       the list. For example a meter can be a length or a distance,
--       length is used as the type and distance is a subtype.
--       A user may provide additional local subtype names for units
--       and thus has the full capability for alternate type names.
--
--   The comments below are organized to present the physical quantity name with
--associated information. The second column is one of the typical symbols used
--for the physical quantity. The third column is the dimension of the physical
--quantity expressed in terms of the fundamental dimensions. The fourth column
--is the name of the unit in the MKS measurement system. The fifth column
--is the typical MKS unit equation. An independent table presents conversion
--factors from the MKS measurement system to other measurement systems.
--   Physics developed over a period of many years by many people from a variety
--of disciplines. Thus, there is ambiguity and duplication of symbols.
--
--
--PHYSICAL QUANTITY         SYMBOL  DIMENSION   MEASUREMENT UNIT  UNIT EQUATION
--_________________         ______  _________   ________________  ______________
--
--
--                                  BASIC UNITS
--
--length                     s       L           meter              m
--wave length                lambda  "             "                "
--
  type LENGTH_MKS is new REAL ;
  subtype LENGTH_METER is LENGTH_MKS ;
  subtype LENGTH_METERS is LENGTH_MKS ;  -- This could be done for every type
  subtype DISTANCE_METER is LENGTH_MKS ;  -- with plurals and alias and
  subtype DISTANCE_METERS is LENGTH_MKS ;  -- plurals for the alias
  subtype WAVE_LENGTH_MKS is LENGTH_MKS ;
  subtype WAVE_LENGTH_METER is LENGTH_MKS ;
  type LENGTH_ENGLISH is new REAL ;
  subtype LENGTH_FOOT is LENGTH_ENGLISH ;
  subtype LENGTH_FEET is LENGTH_ENGLISH ;
  type LENGTH_PICOMETER is new REAL ;
  type LENGTH_NANOMETER is new REAL ;
  type LENGTH_MICROMETER is new REAL ;
  type LENGTH_MILLIMETER is new REAL ;
  type LENGTH_CENTIMETER is new REAL ;
  type LENGTH_DECIMETER is new REAL ;
  type LENGTH_DECAMETER is new REAL ;
  type LENGTH_HECTOMETER is new REAL ;
  type LENGTH_KILOMETER is new REAL ;
  type LENGTH_MEGAMETER is new REAL ;
  type LENGTH_GIGAMETER is new REAL ;
  type LENGTH_ANGSTROM is new REAL ;
  type LENGTH_MIL is new REAL ;
  type LENGTH_INCH is new REAL ;
  type LENGTH_YARD is new REAL ;
  type LENGTH_FATHOM is new REAL ;
  type LENGTH_ROD is new REAL ;
  type LENGTH_CHAIN_SURVEYOR is new REAL ;
  type LENGTH_CHAIN_ENGINEER is new REAL ;
  type LENGTH_FURLONG is new REAL ;
  type LENGTH_MILE is new REAL ;
  subtype LENGTH_MILE_STATUTE is LENGTH_MILE ;
  type LENGTH_MILE_NAUTICAL is new REAL ;
  type LENGTH_LEAGUE_LAND is new REAL ;
  type LENGTH_LEAGUE_MARINE is new REAL ;
  type LENGTH_LIGHT_YEAR is new REAL ;

--
--mass                       m       M           kilogram           Kg
--
  type MASS_MKS is new REAL ;
  subtype MASS_KILOGRAM is MASS_MKS ;
  type MASS_ENGLISH is new REAL ;
  subtype MASS_POUND is MASS_ENGLISH ;
  subtype MASS_POUND_AVDP is MASS_ENGLISH ;
  type MASS_POUND_TROY is new REAL ;
  subtype MASS_POUND_APOTHECARY is MASS_POUND_TROY ;
  type MASS_MILLIGRAM is new REAL ;
  type MASS_GRAM is new REAL ;
  type MASS_GRAIN is new REAL ; -- same inall English systems
  type MASS_PENNYWEIGHT_TROY is new REAL ;
  type MASS_CARAT_TROY is new REAL ;
  type MASS_SCRUPLE is new REAL ;
  type MASS_DRAM_AVDP is new REAL ;
  type MASS_OUNCE_AVDP is new REAL ;
  type MASS_OUNCE_TROY is new REAL ;
  type MASS_TON_SHORT is new REAL ;
  type MASS_TON_LONG is new REAL ;
  type MASS_TON_METRIC is new REAL ;

--
--time                       t       T           second             sec
--
  type TIME_SECOND is new REAL ;
  subtype TIME_SECONDS is TIME_SECOND ;
  type TIME_PICOSECOND is new REAL ;
  type TIME_NANOSECOND is new REAL ;
  type TIME_MICROSECOND is new REAL ;
  type TIME_MILLISECOND is new REAL ;
  type TIME_CENTISECOND is new REAL ;
  type TIME_KILOSECOND is new REAL ;
  type TIME_MEGASECOND is new REAL ;
  type TIME_GIGASECOND is new REAL ;
  type TIME_MINUTE is new REAL ;
  type TIME_HOUR is new REAL ;
  type TIME_DAY is new REAL ;
  type TIME_FORTNIGHT is new REAL ;
  type TIME_MONTH is new REAL ;
  type TIME_YEAR is new REAL ;
  type TIME_DECADE is new REAL ;
  type TIME_CENTURY is new REAL ;
  type TIME_MILLENNIA is new REAL ;

--
--electric charge            q       Q           coulomb            c
--  electric flux
--
  type CHARGE_COULOMB is new REAL ;
  subtype CHARGE_AMPERE_SECOND is CHARGE_COULOMB ;
  type CHARGE_AMPERE_HOURS is new REAL ;
  type CHARGE_ELECTRON is new REAL ;
  type CHARGE_FARADAY is new REAL ;

--
--luminous intensity         I       C           candle             cd
--
  type LUMINOUS_INTENSITY_CANDLE is new REAL ;

--                                                                  o
--temperature                T       K           degree kelvin       K
--
  type TEMPERATURE_KELVIN is new real ;
  type TEMPERATURE_CENTIGRADE is new REAL ;
  subtype TEMPERATURE_CELSIUS is TEMPERATURE_CENTIGRADE ;
  type TEMPERATURE_FARENHEIT is new REAL ;

--
--angle                      theta   none        radian             none
--
  type ANGLE_RADIAN is new REAL ;
  subtype ANGLE_RADIANS is ANGLE_RADIAN ;
  subtype PLANE_ANGLE_RADIANS is ANGLE_RADIAN ;
  type ANGLE_SECOND is new REAL ;
  type ANGLE_MINUTE is new REAL ;
  type ANGLE_DEGREE is new REAL ;
  type ANGLE_REVOLUTION is new REAL ;
  type ANGLE_BAM is new REAL ;

--
--solid angle                phi     none        steradian          none
--
  type SOLID_ANGLE_STERADIAN is new REAL ;
--
end PHYSICAL_UNITS_BASIC ;